On the number of zeros of bounded nonoscillatory solutions to higher-order nonlinear ordinary differential equations

summary:The higher-order nonlinear ordinary differential equation \[ x^{(n)} + \lambda p(t)f(x) = 0\,, \quad t \ge a\,, \] is considered and the problem of counting the number of zeros of bounded nonoscillatory solutions $x(t;\lambda )$ satisfying $\lim _{t\rightarrow \infty }x(t;\lambda ) = 1$ is studied. The results can be applied to a singular eigenvalue problem